Work

Stability and uniqueness of minimal disks in non-constant curvature

Year: 2026

Type: preprint

Abstract: Nitsche proved that every smooth Jordan curve in $\mathbb{R}^3$ of total curvature at most $4π$ bounds a unique minimal disk, which is moreover strictly stable. We prove an analogue of this result for Riemannian $3$-balls with mean convex boundary, under an explicit pinching condition on the negative sectional curvature, together with a bound on the covariant derivative of the Ricci tensor. In this setting, every smooth Jordan curve in the boundary sphere of total curvature at most $4π$ bounds a unique embedded minimal disk which is strictly stable.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.29542

Authors: Alvarez, Sébastien, Lefeuvre, Thibault, Lowe, Ben, Smith, Graham A.

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214394612

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